共查询到20条相似文献,搜索用时 115 毫秒
1.
Peter Tass 《Zeitschrift für Physik B Condensed Matter》1995,99(1):111-121
We analyze two nonlinearly phase coupled oscillators with eigenfrequencies ω1and ω2, where n\gw1=m\gw2+\gp, with integern andm. For \gh=0 there are up to four stable synchronized states which differ from each other only by the difference of the oscillators\rs
phases. The number of different synchronized states depends on the coupling constants. If \gh does not vanish phase shifts
and frequency shifts may occur givig rise to stable synchronized states which also differ from each other due to the frequencies.
By means of the center manifold theorem we calculate these shifts explicitely. Different coupling constants are investigated:
symmetrical, homogenously asymmetrical and arbitrary coupling constants. Our results point out the decisive influence of the
symmetry of the coupling constants upon the frequency and phase shifts. Moreover the local stability of the unperturbed synchronized
state (i.e. for \gh=0) determines the magnitude of the frequency and phase shifts. 相似文献
2.
Liu Yong-Mei 《International Journal of Theoretical Physics》2009,48(8):2372-2378
In this paper, we apply the method of “invariant eigen-operator” to study the Hamiltonian of arbitrary number of coupled identical
oscillators and derive their invariant eigen-operator. The results show that, (1) for the system of arbitrary number of identical
harmonic oscillators by coordinate coupling or momentum coupling, the invariant eigen operator
of system always has the form of
or
; (2) the energy level gap of the system has two kinds of possibilities: one is that gap only related to ω that the frequency of oscillators; another one is that gap not only related to ω that the frequency of oscillators, but also related to the number of the coupling oscillators. 相似文献
3.
The existence and stability of phase-clustered states have been studied previously in networks of weakly coupled oscillators with uniform coupling strengths [Physica D 63 (1993) 424]. However, several studies have shown that if the coupling is uniform and repulsive, it is hard to obtain stable phase-clustered states in networks of realistic neural oscillators when noise is present [Neural Comput. 7 (1995) 307; Phys. Rev. E 57 (1998) 2150]. This problem was avoided by introducing heterogeneity in the distribution of coupling strengths [J. Phys. Soc. Jpn. 72 (2003) 443]. It has been shown that heterogeneous coupling strengths make the occurrence of stable clustered states possible in small networks of repulsively coupled neural oscillators of all kinds [J. Comput. Neurosci. 14 (2003) 139; SIAM J. Appl. Math., submitted for publication]. The present work extends these results to large networks of N identical neurons that are globally coupled with heterogeneous and asymmetrical coupling strengths. Conditions for the existence and stability of a state of n synchronized clusters at evenly distributed phases, called the state of n splay-phase clusters, are derived. Clusters of different sizes, i.e. containing different numbers of neurons, are studied. The existence of such a state is guaranteed if the strength of the coupling originating from one neuron to other neurons is inversely proportional to the size of the cluster to which it belongs. This condition is called the rule of inverse cluster-size. At the state of n splay-phase clusters, the N-neuron network behaves like a network of n “big neurons”. Stability of this state is determined by n eigenvalues of which only one determines the stability of intra-cluster phase differences. The remaining n−1 conditions determine the stability of inter-cluster phase differences, but only nh=(n− mod (n,2))/2 of them have distinct real parts due to symmetry. Heterogeneous coupling makes the stability conditions depend on coupling strengths. This analysis not only reveals how clustered states occur in more general kinds of networks, but also illustrates how the stability of clustered states can be achieved in networks of repulsively coupled neural oscillators. Results on clustered states with phases that are not evenly distributed in the phase space are also presented. Potential applications of these results are discussed. 相似文献
4.
E. V. Kal’yanov 《Technical Physics》2012,57(3):315-319
The influence of the asymmetry of the nonlinear element characteristic on the chaotic oscillations of Chua’s bistable oscillator
is studied. It is shown that such asymmetry causes asymmetry of a chaotic attractor that maps the switching of motions between
two basins of attraction up to the concentration of oscillations in one basin. Oscillation control in a bistable chaotic self-oscillating
system (two coupled Chua’s oscillators) is considered. It is demonstrated that oscillations excited in two basins of attraction
may pass to one of them and that oscillations may build up in two basins when they are autonomously excited in different basins.
It is also found that chaotic oscillations in a coupled system may be excited at parameter values for which the autonomous
chaotic oscillations of partial oscillators are absent. The influence of external noiselike oscillations is investigated. 相似文献
5.
We stress that in contradiction with what happens in space dimensions n ≥ 3, there is no strict bound on the number of bound states with the same structure as the semi-classical estimate for a
large coupling constant. We give, in two dimensions, examples of weak potentials with one or infinitely many bound states.
We derive bounds for one and two dimensions which have the “right” coupling-constant behaviour for large coupling.
Received November 22, 2001; accepted for publication November 28, 2001 相似文献
6.
The processes of cluster formation in liquid alcohols, water, methanol, n-hexanol, and n-hexane have been investigated by the method of flicker-noise spectroscopy. Two types of clusters — clusters with a close-packed
structure and clusters with a loose structure — have been detected. The energy of formation of different clusters in methanol
and n-hexane ranges, respectively, from −250 to +250 J/mole and from −50 to +50 J/mole. The smallest clusters of methanol, n-hexanol, water, and n-hexane consist, respectively, of six, two, eleven, and two molecules, and their largest clusters represent oscillators consisting,
respectively, of 50,400, 17,200, 93,500, and 33,150 molecules at 274 K. In methanol at 271 K, more than 44 types of clusters
consisting of 6, 97, 152, 219, 297, 492, 1029, 1368, 1560, etc. molecules were detected. In n-hexanol at 273 K, 57 types of clusters were detected. Models of small clusters are proposed. In water, the content of close-packed
clusters is maximum at 277 K. The energy of formation/decomposition of small clusters in water ranges from −0.4 to +0.4 kJ/mole
and increases with increase in the water temperature. The hysteresis of transformation of the (H2O)280 cluster in the process of heating and cooling of water in the temperature range 273–280 K was detected. Series of energy
spectra of clusters in liquids at different temperatures are presented and discussed.
__________
Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 3, pp. 305–312, May–June, 2005. 相似文献
7.
In this paper we present explicit and simple analytical formulae for the energy eigenvaluesE
n (λ) of one-dimensional anharmonic oscillators characterized by the potentials 1/2mω
2
x
2+λx
2α withα=2, 3 and 4. A simple intuitive criterion supplemented by the requirement of correct asymptotic behaviour, has been employed
in arriving at the formulae. Our energy values over a wide range ofn andλ are in good agreement with the numerical values computed by earlier workers through very elaborate techniques. To our knowledge
this is the first time that formulae of such wide validity have been given. The results for pure power oscillators are trivially
obtained by going over to theω→0 limit. Approximate analytic expressions for the low order even moments ofx are also given. 相似文献
8.
V. Yo. Stadnyk M. O. Romanyuk B. V. Andrievsky Z. O. Kogut 《Optics and Spectroscopy》2010,108(5):753-760
The influence of uniaxial pressure applied along the principal crystallophysical directions on the dispersion and temperature
dependences of the refractive indices n
i
of K2ZnCl4 crystals has been investigated. The n
i
values are found to be fairly sensitive to uniaxial pressure, whereas an uniaxial stress does not change the behavior of
the dispersion and temperature dependences of n
i
. The baric changes in n
i
have been studied. The electronic polarizability α
i
, refractions R, and parameters of UV oscillators (λ0i
, B
1i
) of mechanically deformed K2ZnCl4 crystals have been calculated. The contributions of UV and IR oscillators to n
i
(λ) have been estimated for different temperatures, spectral regions, and stresses. A significant baric shift of the points
of the paraelectric phase-incommensurate phase-commensurate phase transitions to different temperature ranges, depending on
the direction of pressure application, is found; this shift is due to the effect of uniaxial stress on the K2ZnCl4 crystal structure. 相似文献
9.
Summary The structure of water in water/AOT/n-heptane reverse micelles has been studied as a function of the [H2O]/[AOT] ratio (W) by using the absorption IR due to O−H stretching modes in the 3800–3000 cm−1 range. The results show that the IR spectra can be expressed as a sum of contributions from bound- and bulk-like water. The
fraction of water in the two ?regions? within the water pool was evaluated as a function ofW. The ?bound? water region seems to hold 3.5 water molecules (corresponding to 7 O−H oscillators) per AOT molecule and its
formation is nearly complete atW>6.
Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994. 相似文献
10.
Y. Zhang H.A. Cerdeira G. Hu 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,23(1):97-102
A ring of diffusively coupled R?ssler oscillators, which can develop the conventional rotating wave from high-dimensional
chaos by increasing the coupling ɛ continuously is studied. The chaotic generator for the rotating wave emerges around ɛ =
ɛ, where the topological transition induced by the coupling not only changes the topological structure of all the oscillators,
which share a common strange attractor, but also changes them into being different from each other. Starting from this transition,
infinitely long range temporal correlation and spatial order in the style of antiphase state are established gradually, which
gives rise to the chaotic generator of the rotating wave.
Received 15 March 2001 相似文献
11.
A braided subfactor determines a coupling matrix Z which commutes with the S- and T-matrices arising from the braiding. Such a coupling matrix is not necessarily of “type I”,
i.e. in general it does not have a block-diagonal structure which can be reinterpreted as the diagonal coupling matrix with
respect to a suitable extension. We show that there are always two intermediate subfactors which correspond to left and right
maximal extensions and which determine “parent” coupling matrices Z
± of type I. Moreover it is shown that if the intermediate subfactors coincide, so that Z
+=Z
−, then Z is related to Z
+ by an automorphism of the extended fusion rules. The intertwining relations of chiral branching coefficients between original
and extended S- and T-matrices are also clarified. None of our results depends on non-degeneracy of the braiding, i.e. the
S- and T-matrices need not be modular. Examples from SO(n) current algebra models illustrate that the parents can be different, Z
+≠Z
−, and that Z need not be related to a type I invariant by such an automorphism.
Received: 8 December 1999 / Accepted: 15 February 2000 相似文献
12.
B. A. Magradze 《Few-Body Systems》2006,40(1-2):71-99
Recently, the QCD renormalization-group (RG) equation at higher orders in MS-like renormalization schemes has been solved
for the running coupling as a series expansion in powers of the exact two-loop-order coupling. In this work, we prove that
the power series converge to all orders in perturbation theory. Solving the RG equation at higher orders, we determine the
running coupling as an implicit function of the two-loop-order running coupling. Then we analyze the singularity structure
of the higher-order coupling in the complex two-loop coupling plane. This enables us to calculate the radii of convergence
of the series solutions at the three- and four-loop orders as a function of the number of quark flavours n
f
. In parallel, we discuss in some detail the singularity structure of the
coupling at the three- and four-loops in the complex-momentum squared plane for 0 ≤ n
f
≤ 16. The correspondence between the singularity structure of the running coupling in the complex-momentum squared plane
and the convergence radius of the series solution is established. For sufficiently large n
f
values, we find that the series converges for all values of the momentum-squared variable Q
2 = −q
2 > 0. For lower values of n
f
, in the
scheme, we determine the minimal value of the momentum-squared Q
min
2 above which the series converges. We study properties of the non-power series corresponding to the presented power-series
solution in the QCD analytic perturbation-theory approach of Shirkov and Solovtsov. The Euclidean and Minkowskian versions
of the non-power series are found to be uniformly convergent over the whole ranges of the corresponding momentum-squared variables. 相似文献
13.
M HOSSEINI FARZAD 《Pramana》2012,78(4):595-612
Optical parametric amplification (OPA) described usually by the coupled-wave equations with the first-order derivatives of
the signal and idler waves, is solved under the slowly-varying amplitude approximation (SVA). In this article, by keeping
the second-order derivatives in the coupled-wave equations, we obtained an analytical solution for the output signal and idler
waves up to the first order of (κ/k)1; the ratio of coupling constant to the wave number. Furthermore, here the signal and the idler waves are distinguished only
by their polarizations with the same frequency. Light squeezing is observed in normally ordered variances of the two quadrature
operators of the output combined mode when plotted against κL, where κ is the coupling constant and L the interaction length. The variances have different signs for a range of values of κL and their variations are in opposite directions. We also show that this property is strongly dependent on the relative refractive
index of the medium (n). It is worth mentioning that the relative index dependency is not an explicit feature in squeezing of OPA under SVA approximation.
Furthermore, the squeezing vanishes when n → 1 and κ/k → 0. 相似文献
14.
We consider a chain of N harmonic oscillators perturbed by a conservative stochastic dynamics and coupled at the boundaries to two gaussian thermostats
at different temperatures. The stochastic perturbation is given by a diffusion process that exchange momentum between nearest
neighbor oscillators conserving the total kinetic energy. The resulting total dynamics is a degenerate hypoelliptic diffusion
with a smooth stationary state. We prove that the stationary state, in the limit as N→ ∞, satisfies Fourier’s law and the linear profile for the energy average 相似文献
15.
In this paper, we present the metric for the n-dimensional charged slowly rotating dilaton black hole with N = [(n −1)/2] independent rotation parameters, associated with N orthogonal planes of rotation in the background of asymptotically flat and asymptotically (anti)-de Sitter spacetime. The
mass, angular momentum and the gyromagnetic ratio of such a black hole are determined for the arbitrary values of the dilaton
coupling constant. We find that the gyromagnetic ratio crucially depends on the dilaton coupling constant, α, and decreases with increasing α in any dimension. 相似文献
16.
N. Rubido C. Cabeza S. Kahan G.M. Ramírez Ávila Arturo C. Marti 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2011,62(1):51-56
Stable synchronous states of different order were analytically, numerically and
experimentally characterized in pulse-coupled light-controlled oscillators (LCOs). The
Master-Slave (MS) configuration was studied in conditions where different time-scale
parameters were tuned under varying coupling strength. Arnold tongues calculated
analytically – based on the piecewise two-time-scale model for LCOs – and obtained
numerically were consistent with experimental results. The analysis of the stability
pattern and tongue shape for (1 : n) synchronization was based on the
construction of return maps representing the Slave LCO evolution induced by the action of
the Master LCO. The analysis of these maps showed that both tongue shape and stability
pattern remained invariant. Considering the wide variation range of LCO parameters, the
obtained results could have further applications on ethological models. 相似文献
17.
We report measurements of ∂m/∂n in Si MOSFET, where m is the magnetization of the two-dimensional electron gas and n is its density. We extended the density range of measurements from well in the metallic to deep in the insulating region.
The conditions under which this extension is justified, as well as the corrections that should be made to extract ∂m/∂n properly, are discussed in detail. At low temperatures, ∂m/∂n was found to be strongly nonlinear already in weak magnetic fields, on a scale much smaller than the characteristic scales,
expected for interacting two-dimensional electron gas. Surprisingly, this nonlinear behavior exists both in the dielectric,
and in the metallic region. These observations, we believe, provide evidence for strong coupling of the itinerant and localized
electrons in Si-MOSFET. 相似文献
18.
Energy eigenvalues and 〈x
2〉
n
for the oscillators having potential energyV(x)=(ω
2
x
2/2)+λ<x
2r
>x
2s
have been determined for various values ofλ, r, s andn using renormalized hypervirial-Padé scheme. In general, the results show an improvement over the findings of earlier workers.
Variation of the evaluated quantities and of the renormalization parameter withλ, r, s andn has been discussed. In addition, this potential has been employed as an illustrative example of the applicability of alternative
formalism of perturbation theory developed by Kim and Sukhatme (J. Phys.
A25 647 (1992)). 相似文献
19.
The forward neutron production in the ep collisions at 300GeV measured by H1 and ZEUS Collaborations at DESY has been used to estimate the total probability for proton
fluctuation into nπ+ and pπ0. The probability found is on the order of 30%. This number is compared with the numbers obtained for the probability of quark
fluctuation into π+ from several alternative DIS processes (Gottfried sum rule, polarized structure function) and the axial-vector coupling constant,
where the pion fluctuation is believed to play an important role. 相似文献
20.
Previous results on local asymptotic normality (LAN) for qubits [16, 19] are extended to quantum systems of arbitrary finite
dimension d. LAN means that the quantum statistical model consisting of n identically prepared d-dimensional systems with joint state converges as n → ∞ to a statistical model consisting of classical and quantum Gaussian variables with fixed and known covariance matrix,
and unknown means related to the parameters of the density matrix ρ. Remarkably, the limit model splits into a product of a classical Gaussian with mean equal to the diagonal parameters, and
independent harmonic oscillators prepared in thermal equilibrium states displaced by an amount proportional to the off-diagonal
elements. As in the qubits case [16], LAN is the main ingredient in devising a general two step adaptive procedure for the
optimal estimation of completely unknown d-dimensional quantum states. This measurement strategy shall be described in a forthcoming paper [18]. 相似文献